Abstract
We analyze a wide class of penalty energies used for contact response through the lens of a reduced frame.
Applying our analysis to both spring-based and barrier-based energies, we show that we can obtain closed-form,
analytic eigensystems that can be used to guarantee positive semidefiniteness in implicit solvers.
Our approach is both faster than direct numerical methods, and more robust than approximate methods
such as Gauss-Newton. Over the course of our analysis, we investigate physical interpretations for two separate
notions of length. Finally, we showcase the stability of our analysis on challenging strand, cloth, and
volume scenarios with large timesteps on the order of 1/40 s.
Main Assets
Raw Videos
Strand Stretching - tests with two sets of strands pulling against eachother
Cloth Stretching - tests with two sheafs of cloth pulling against eachother
Hammock Drop - tests where several sheets collide with a hammock
Volume Filter - a demonstration on why filters are necessary for collision penaty Hessians
Acknowledgemenets
We thank the reviewers for their comments. This work was supported by Adobe,
the Bungie Foundation, Teng and Han Family Fund, and National Science Foundation
(IIS-2132280). Any opinions, findings, and conclusions or recommendations expressed
in this material are those of the authors and do not necessarily reflect the views
of the National Science Foundation.
